The classical theorem of Mntz and Szsz says that the span ofis dense in C[0,1] in the uniform norm if and only if . We prove that, if {i} is lacunary, we can replace the underlying interval [0,1] by any set of positive measure. The key to the proof is the establishment of a bounded Remez-type inequality for lacunary Mntz systems. Namely if A [0,1] and its Lebesgue measure (A) is at least > 0 thenwhere c depends only on and (not on n and A) and where :=infii+1/i>1.
